Analysis of gray markets in differentiated duopoly

In recent years, gray markets have become a significant phenomenon in the business practice. This paper investigates the gray markets issues in differentiated duopoly case by considering quantity competition among firms. We develop a game-theoretic model and provide equilibrium results for three scenarios, i.e. the benchmark scenario 'no gray market', the scenario 'parallel imports act as a buffer against a follower's product' and the scenario 'gray markets stimulate the competition'. By the analysis of the equilibrium results, some important managerial insights are obtained. Finally, by comparison of the equilibrium results among different scenarios, we study the impact of gray markets on manufacturers' optimal strategies and profits in differentiated duopoly.